MICRO/NANO-MANIPULATORS WITH STRUCTURED PIEZO

CERAMIC ACTUATORS

R. Kasper

, M. Al-Wahab

, K. Kostadinov

and T. Tiankov

Institute of Mobile Systems, Otto-von-Guercke University, 2 University Square, Magdeburg, Germany

Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 4, 1113, Sofia, Bulgaria

Keywords: Structured piezo-ceramics, Micro, Nano, Manipulators.

Abstract: This paper presents an investigation and development of mechatronic handling devices (MHD) based on a

structured piezo ceramic with (3, 1)-piezoelectric effect for manipulation and processing of micro/nano

operations. Following the synthesis of kinematic structure for micro- and nano-manipulation tasks based on

structured piezo ceramics and closed kinematic structures, a specific multilayer design of piezo actuated

MHD for micro-and nano-operations was developed. The MHD was mathematically modelled and a FE–

model was created and simulated with the program system ANSYS. Comparison study of the MHD

prototypes was performed using obtained experimental results. An experimental set up was created that

aimed to verify the mathematical and simulation models measuring system behaviour like force,

displacement and stiffness.

1 INTRODUCTION

Micro and nano manipulators are used in different

fields; e.g. in micro assembly, medicine, genetics,

cellular biology technology, chemistry, investigation

of thin films, atomic force microscopes (AFM) and

scanning tunnelling microscopes (STM).

There are known micromanipulators with piezo

actuators (Kortschack, 2005; Albut, 2003; Klocke,

1998). PZT actuators offer substantial advantages

for biological cell manipulation such as large force,

high frequency and a small size of displacement

(Patentschrift Hoerbiger Fluidtechnik, 1993; Lubitz,

2000). Other application fields involve typical

manipulations such as cell penetration, cell sorting

and moving or treating microorganisms. Critical

issues in this case are speed of cell penetration,

optimal stroke for penetration or operation,

orientation of the end-effector, working space, and

size of the device itself.

The increasing requirements of high precision

equipment in the fields above perform a broad

spectrum of handling and manipulation tasks which

is a prerequisite for searching for new concepts of

investigation of piezo-actuated mechatronic

handling devices.

Utilizing the technological capacity for rapid

prototyping of mechatronic systems based on the

piezo-structured ceramics, and the improvement of

such systems is a prerequisite for the development of

technology for manufacturing of mechatronic

handling devices (MHD) that are able to perform a

certain user-requested micro- or nano-operation. The

past general use of piezo-actuators in a direction of

motion (3, 3 or 3, 1) is to be extended for realization

of piezo-structures for the operation tasks (Kasper,

2006; Kasper, 2004; Chakarov, 2006).

By structuring ceramics as well as stacking and

combining them with further elements, more piezo-

actuators axis motions are subjected for

development. To produce movement parameters by

combining various possibilities of structuring with

appropriate servo-mechanism, which is currently

realisable with very complex and large systems, is a

promising design approach (Bar-Itzhack, 2000;

Kostadinov, 2006; Kostadinov, 2005) for which the

following four parameters are significant for

determination of the reference task function of any

mechatronic handling device:

The first parameter is the stroke. The desired

goal is an adjustment of the stroke of approximately

100 μm in all 3 directions X, Y and Z.

The second parameter is the force. It is well-

known that stack actuators produce forces within the

kN range, and bending transducers deliver forces up

to 1 N. Neither stack actuators, nor bending

242

Kasper R., Al-Wahab M., Kostadinov K. and Tiankov T..

MICRO/NANO-MANIPULATORS WITH STRUCTURED PIEZO CERAMIC ACTUATORS.

DOI: 10.5220/0003539202420247

In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2011), pages 242-247

ISBN: 978-989-8425-75-1

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

transducers are here optimally suitable. The

possibilities of structuring piezo ceramics with

consideration of the generation of the stroke can be

helpful in this case. Therefore, it is possible to

optimize stroke and force in one design.

The third parameter is the size. The actuator for

the generation of movement must be integrated into

the MHD. The building area is limited. Thus, both

piezo plates and piezo disks can be used as raw

material. The characteristics of piezo materials are to

be selected in such a way that reaches desired

parameters for stroke and force.

The fourth parameter is the load speed. The

structure of the piezo ceramic must be designed in

such a way that the desired dynamics of the

movement can be achieved. The intended speeds lie

within the range of approximately 200μm/ms.

Thereby, an optimization is necessary in this case

too. Emphasis is the joint action of piezo ceramic

and servo-mechanism system. The servo-mechanism

system has to be adapted to the desired parameters

for stroke and force.

2 CLOSED KINEMATIC

STRUCTURES BASED

ON PIEZO CERAMICS

Piezo-structured ceramics, MHD using piezo stack

actuators and single ceramic actuators could be

assumed by the mechanism and machine theory as a

mechanism with closed kinematic structures. The

polarized ceramic elements, piezo stack actuators

and single ceramic actuators can be estimated as

actuators for linear motion, which can be modelled

by the kinematic chain as shown in Figure1 (Kasper,

2004, Chakarov, 2006).

Figure 1: Kinematic scheme of MHD.

MHD for micro- and nano-manipulation tasks

shown in figure 1 is characterized with 3 degrees of

freedom (DOF) and 6 piezo actuators. The double

sided system is built from a base plate with three

piezo actuators on each side which are arranged at

an angle of 120° using spherical joints.

3 MATHEMATICAL

MODELLING OF A MHD

FOR MICRO AND NANO

APPLICATION

Following the synthesis of the kinematic structure,

the design of a double sided MHD based on

structured piezo actuators with integrated

displacement amplifier was mathematically

modelled and calculated.

Starting from the kinematic scheme given in

Figure 1 a mechanical model of the MHD shown in

Figure 2 was built taking into account relevant

constraints resulting from construction and

manufacturing. On each side of a fixed circular base

plate, 3 piezo-actuators are connected with a ball

joint in a vertical distance h from points R

1÷3

located

in XY-plane at a distance R from the origin.

Vectors

⎥

⎦

⎤

⎢

⎣

⎡

−

))1(3/2cos(

))1.(3/2sin(

. k

for k=1÷3 (1)

from origin to point R

1÷3

are symmetrically

distributed at angles .

Figure 2: Mechanical Model of the MHD.

The pointer of the MHD is fixed at point B of

bottom plate and led through point A of top plate to

the TCP defined by point P. Vectors r

A1÷A3

at top

plate and r

B1÷B3

at bottom plate are constructed

similar to vectors r

1÷3

at base plate with r the radius

of top and bottom plate.The pointer can be split into

MICRO/NANO-MANIPULATORS WITH STRUCTURED PIEZO CERAMIC ACTUATORS

243

two vectors

ABb =

and

APa =

with fixed length

and

. Using Cardan angles φ, ψ and θ

the orientation of the pointer, top and bottom plate is

defined by the rotation matrix T(φ, ψ,

θ)=T

(φ).T

(ψ).T

(θ) built by elementary rotations

(φ), T

(ψ) and T

(θ) of X, Y and Z-axis

(Chakarov, 2006). Coordinates of the TCP are given

⎥

⎦

⎤

⎢

⎣

⎡

zba

(2)

where x and y are absolute coordinates and z defines

the difference to the zero position, when there are no

rotations and bottom and top plate have a distance of

b/2 to the base plate. Vectors defining the position

and orientation of the piezo-actuators are given by

kAkAk

rhraPl

−−+−=

for k=1÷3

for the upper ones and

kBkBk

rhrbaPl

−+++−=

for k=1÷3

for the lower ones. As a result of the construction,

actuators are joined to the base plate in a vertical

distance h, leading to

ehh .=

, with

the unit

vector in Z-direction. Modelling a piezo-actuator as

a massless elastic bar, its force at the end points can

be written as:

lllllcF /)..(

Δ+−= . (3)

For each actuator

has to be replaced by its

individual vector

31÷A

l or

31÷B

l respectively. From

geometry, the forceless length of all actuators is

))()2/((

rRhbl −+−= (4)

The spring constant c of each actuator can be

approximated by c=A.E/l

with the actuator’s

elasticity module E and sectional area A. The

elongation Δl=(A.d

).U is driven by the control

voltage U, with piezoelectric constant d

, which is

negative for the 3,1 effect utilized in this application.

In the control system, voltages U

, U

and U

of the

upper actuators can be driven individually, whereas

only one voltage U

is used to control the 3 lower

actuators. To calculate the 3 actual position

coordinates x, y and z as well as the 3 orientation

angles φ, ψ and θ the principle of equilibrium of

forces

∑

=++=Δ

0)(

TCPBkAk

FFFF (5)

and torques

∑

=×+×+=Δ

0))((

TCPBkBk

FaFrbM

(6)

are used. Here

TCP

is external force acting at the

TCP. These 6 equations can be solved e.g.

numerically by minimizing the square of the

residuals

MinMF →Δ+Δ

(7)

using LSSOLVE method from Maple’s optimization

package. To achieve residuals of 10

-12

and below,

less than a second of computation time is needed

starting from pointer’s zero position as initial values.

Thus, computational speed is high enough to use this

model to adapt geometric and material data of the

MHD to fulfil the design goals. The resulting

parameters are given in Table 1:

Table 1: MHD geometric and material parameters.

Parameters free to improve design goals

A a B E

37.5mm² 49.5mm 10.5mm 80kN/mm²

Parameters fixed by construction

R h R d

40mm 4mm 7.5mm 18e-8

4 FEM-SIMULATIONS OF A

MHD FOR MICRO- AND

NANO-MANIPULATION

TASKS BASED ON

STRUCTURED PIEZO

CERAMICS AND CLOSED

KINEMATIC STRUCTURE

FE-model of MHD for micro- and nano-

manipulators based on the kinematic scheme with 3

DoF shown in Figure 2 was created and simulated.

The FE-model is presented in Figure 3. The system

is pre-strained within itself. That gives the

possibility for 3D motion on the end effector and

makes the joints free from backslash. Applying the

same control voltage to 3 actuators in the bottom; a

movement with 90° to the basic surface (Z-axis) can

be reached. If a different control voltage on the other

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

244

three actuators is applied, it is possible to get

movements on X, Y and Z directions. The

arrangements of the actuators are seen in Figure 4.

The results given in Figure 5 are calculated in FE

simulation for PZT with a thickness of 1.5 mm. FE-

models built up using ANSYS allow the coupled

treatment of mechanical and piezo-electrical effects.

Attention has been paid on nonlinear effects in

geometry of the motion amplification system and its

connection elements to the piezo-ceramic base plate.

At the first step, the actuator (A1) was charged and

discharged at a voltage of 800 V.

The second and third steps were when charging

and discharging the actuators (A2) and (A3) in a

similar way. The fourth step was applying the same

control voltage to the bottom three actuators (A456).

Figure 3: Double-sided MHD FE-model.

Figure 4: Arrangement of the upper Piezo-actuators A1,

A2 and A3 of the Double-sided MHD.

A movement perpendicular to the basic surface

(Z-axis) was then reached. The results of the FE

method are given in the figure below.

As expected, we get a displacement in Z

direction around 130 µm and a force of 100 N is

generated.

Co-operating all 3 actuators with different linear

extension, it is possible to permit an exact

positioning of the end effector in the work space.

5 STUDY AND DESIGN

OF THE DEVELOPED

PROTOTYPES OF MHDS

To verify the mathematical and the FE- models, a

prototype of MHD for micro- & nano-manipulators

based on the kinematic scheme in Figure 1 was

developed. The steel plate (left top Figure 6) has an

immovable base which is connected by spherical

joints to the actuating lever.

Figure 5: FE Simulation Results of the Double-sided

MHD.

Figure 6: MHDs Prototype.

The necessary operating voltage is determined by

the actuator’s thickness. To reduce it, the actuator

MICRO/NANO-MANIPULATORS WITH STRUCTURED PIEZO CERAMIC ACTUATORS

245

can be produced from several layers. In our case the

prototype has been developed from Piezo plate (3, 1

effect) with thickness equal to 0.5 mm. Every

actuator has 3 layers where a control with max.1000

V is necessary. Finally, a prototype was designed

and manufactured (Figure6).

An experimental set-up based on digital

microscopy and software application (Shulev, 2010)

for the prototype’s control was used for the

experimental investigation.

The experiments were taken analogously to the

simulations with the Maple and FEM models. As a

scanning, a point on the top of the end-effector is

chosen. The experiments were performed with a

microscope and camera visualization.

The motion of the scanning point has been

studied separately along each axis according to the

control equation below.

⎥

⎦

⎤

⎢

⎣

⎡

⎥

⎦

⎤

⎢

⎣

⎡

⎥

⎦

⎤

⎢

⎣

⎡

zzzz

yyy

U U U U

U U U

U U

4321

321

(8)

Pictures of the probe were taken after each step

of changing the control voltage in order to determine

the displacement in the X, Y and Z direction. Since

the scanning point is actuated by Piezo-elements

with open-loop control system, it is of great

importance to know the specific behaviour of each

piezo element and the motion characteristic.

Figure 7: Experimental Results of the Double-sided MHD.

Therefore, an experimental result was obtained

from each one. The FEM model was solved with the

obtained piezo motions that are in the range of 0 to 9

μm. The dynamic frequency and repeatability of the

developed system are under investigation as well.

The results are given in Figure 7.

The experimental results were summarized and

compared with the simulated and mathematically

calculated data. The summarized results are given in

the table 2.

Table 2: Summarized Results.

Step

[B]

Displace-

ment

X [µm]

[D]

Displace-

ment

Y [µm]

[F]

Displace

ment

Z [µm]

Maple

31 0 -18

FEM

28 =0 -18

Exp.

Results

18 0 -

Maple

-16 27 -18

FEM

-13 24 -18

Exp.

Results

-10 19 -

Maple

-16 -27 -23

FEM

-13 -24 -18

Exp.

Results

-13 -23 -

(A456)

Maple

0 0 119

FEM

0 0 118

Exp.

Results

- - 110

The differences between measurements,

calculations and FEM were due to inaccuracies in

the production of the individual elements and in the

measurements, as well as the deviation of the real

MHD prototype from the adopted mathematical and

FEM models. However, it has been proven that the

prototype showed very similar data in the

experimental tests.

6 CONCLUSIONS

The development of mechatronic handling devices

(MHD) based on a structured piezo ceramic with (3,

1)-piezoelectric effect for manipulation and

processing of micro/nano operations was

investigated. Following the synthesis of kinematic

structure for micro- and nano-manipulation tasks

based on structured piezo ceramics and closed

kinematic structures, a specific multilayer design of

piezo actuated mechatronic handling devices for

micro-and nano-operations was developed. The

system was mathematically modelled, and a FE–

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

246

model was created and simulated with the program

system ANSYS.

A comparison study of the mechatronic handling

device prototypes was performed using obtained

experimental results. An experimental set-up was

used specially created for investigation of such

micro robots.

The mathematical and simulation models were

verified, as well as the system of its behaviour

(force, displacement and stiffness). It has been

proven that the prototype showed very similar data

in the experimental tests to the theoretical data.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the partially

support through the projects:

MeCHa-PiCS project funded by the DFG under

the contract KA-2 “Mechatronic handling devices

based on piezo-ceramic structures for micro- and

nano-applications” and

SpeCy-MiNT project funded by Bulgarian

Science Fund under the Contract Nr. DO

0171/16.12.2008 “Specialized Mechatronic Systems

for Micro and NanoTechnology”.

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